Density of states in structurally disordered 1D chains of atoms

A one-dimensional potential, V(x), assumed to be a sum of δ-Dirac peaks at atom positions is considered. Disorder is introduced by more or less irregular arrangements of atoms’ positions. Alternatively, a binary alloy is considered to be made up of two different potentials of atoms randomly distributed on a regular lattice. Disorder parameters are used to describe the degree of disorder in the system, and the density of states, ρ(E)’ is discussed for various sets of the model parameters and various degrees of disorder. In a limit case of a one-dimensional crystal, analytical results of the Kronig–Penney model serve as a test for computer simulations based on counting zeros of the wave function at a given energy. Simulations have been carried out for both amorphous and chemical disorders, for chains of up to N = 10 000 atoms. The results are discussed in terms of how the density of states is modified by a change in the order parameter, leading for example to the disappearance of the band gap, new localized states emerging, or smearing off and/or shifting of the band edges.